We consider a class of non-linear integro-differential equations describing microfluidic measurements. We prove that under reasonable conditions, solutions to these equations are convex functions of a flow-rate parameter $\xi$ used in metrology. The key elements of our analysis are: (i) elevation of $\xi$ to an independent variable through reformulation of the problem as a partial-differential equation (PDE); and (ii) extension of techniques from the theory of ordinary differential equations to the PDE setting.

中文翻译：

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测量微流体流速：单调性，凸性和不确定性

我们考虑了一类描述微流体测量的非线性积分微分方程。我们证明在合理的条件下，这些方程的解是流量参数的凸函数$\xi$用于计量。我们分析的关键要素是：（i）海拔高度$\xi$通过将问题重新公式化为偏微分方程（PDE），得到一个自变量；（ii）将技术从常微分方程的理论扩展到PDE设置。